If a² + b² + c² + 3 = 2(a + b + c) then the value of (a + b + c) is?

$$\eqalign{ & {a^2} + {b^2} + {c^2} + 3 = 2\left( {a + b + c} \right) \cr & \Rightarrow {a^2} + {b^2} + {c^2} + 3 = 2a + 2b + 2c \cr & \Rightarrow {a^2} - 2a + 1 + {b^2} - 2b + 1 + {c^2} - 2c + 1 = 0 \cr & \Rightarrow {\left( {a - 1} \right)^2} + {\left( {b - 1} \right)^2} + {\left( {c - 1} \right)^2} = 0 \cr & a = 1 \cr & b = 1 \cr & c = 1 \cr & \therefore \left( {a + b + c} \right) \cr & = 1 + 1 + 1 \cr & = 3 \cr} $$